Decision Feedback Equalizers (DFEs) are used in digital telecommunication systems to remove the effects of inter-symbol interference (ISI) caused by linear, or even non-linear, distortions present in the channel, transmit and receive devices.
The DFE operates by subtracting a compensation factor from the incoming, distorted signal. This compensation factor is a weighted sum of past digital decisions, and varies for each input signal instance. Practical DFEs use a limited number of past digital decisions to compute the current compensation factor. There are thus a finite number of compensation factors that can be applied, limited by the number of digital combinations that are allowed by the number of past decisions used to generate the compensation factor for each baud received.
Many different implementations exist for these equalizers. Of particular interest for this disclosure is the unrolled DFE, such as described in S. Kasturia, Techniques for High-Speed Implementations of Nonlinear Cancellation, IEEE Journal on Selected Areas in Communication, Vol. 9, No. 5, June 1991, which is incorporated herein by reference.
The unrolled DFE structure, instead of collecting the input signal and subtracting the compensation factor from it, pre-computes all the possible compensation factors, and each of them is applied as a decision threshold for a single sampler.
This thus requires as many samplers as there are possible decision thresholds. As a result, one digitized output is produced per sampler, that is, one digitized output per compensation factor. These outputs correspond to possible DFE decisions, each being the correct decision for the current bit given a certain pervious history. The DFE then selects which of these outputs corresponds to the correct threshold according to the previous decisions. This simplifies the processing in comparison to a system that computes the DFE compensation from digitized samples of an analog-to-digital (A/D) converter, as the subtraction of the compensation is already performed at the sampling head.
Known implementations of DFEs suffer from an exponential increase in complexity as the number of previous decisions used to compute the current threshold (the DFE depth) is increased.
When compared to systems where the input is first sampled by an ADC and the equalization is computed from the digitized input code, unrolled DFEs can reduce the number of samplers required when the DFE depth is small. However, since the number of samplers required grows exponentially with the DFE depth, this advantage quickly disappears as a larger equalization depth is required.
This reduces the benefits of the simpler computation required by unrolled DFE systems, and limits their application to a small DFE depth.
Improvements in unrolled DFE performance are desirable.